Given,
Angle between pass axis of polarizer and analyser, $\mathrm{\theta } = 45°$ 

Using formula,
                          $\boxed{\mathrm{I} = {\mathrm{I}}_0 {\cos }^2\mathrm{\theta }}$ 

$\Rightarrow$                     $\mathrm{I} = {\mathrm{I}}_0(\cos 45°{)}^2$ 

$\Rightarrow$                      $\mathrm{I} ={\mathrm{I}}_0{\left(\frac{1}{\sqrt{2}}\right)}^2$ 

$\Rightarrow$                      $\frac{\mathrm{I}}{{\mathrm{I}}_0} = \frac{1}{2}$ 

i.e.,                    $\mathrm{I} : {\mathrm{I}}_0 = 1:2.$ 

is the required ratio of intensities of original light and transmitted lightafter passing through the analyzer.